A p-adic probability logic

作者：Ilic Stepic Angelina^*; Ognjanovic Zoran; Ikodinovic Nebojsa; Perovic Aleksandar

来源：Mathematical Logic Quarterly, 2012, 58(4-5): 263-280.

DOI：10.1002/malq.201110006

• probability logic
• p-adic numbers
• [msc2010]03B48
• 68T27

In this article we present a p-adic valued probabilistic logic L-Qp which is a complete and decidable extension of classical propositional logic. The key feature of L-Qp lies in ability to formally express boundaries of probability values of classical formulas in the field Q(p) of p-adic numbers via classical connectives and modal-like operators of the form K-r,K-rho. Namely, L-Qp is designed in such a way that the elementary probability sentences K-r,K-rho alpha actually do have their intended meaning-the probability of propositional formula a is in the Qp-ball with the center r and the radius.. Due to modal nature of the operators K-r,K-rho alpha it was natural to use the probability Kripke like models as L-Qp-structures, provided that probability functions range over Q(p) instead of R or *R.

• 出版日期2012-8